The $W_{1+\infty }$ effective theory of the Calogero- Sutherland model and Luttinger systems.

Abstract

We construct the effective field theory of the Calogero-Sutherland model in the thermodynamic limit of large number of particles $N$. It is given by a $\winf$ conformal field theory (with central charge $c=1$) that describes {\it exactly} the spatial density fluctuations arising from the low-energy excitations about the Fermi surface. Our approach does not rely on the integrable character of the model, and indicates how to extend previous results to any order in powers of $1/N$. Moreover, the same effective theory can also be used to describe an entire universality class of $(1+1)$-dimensional fermionic systems beyond the Calogero-Sutherland model, that we identify with the class of {\it chiral Luttinger systems}. We also explain how a systematic bosonization procedure can be performed using the $\winf$ generators, and propose this algebraic approach to {\it classify} low-dimensional non-relativistic fermionic systems, given that all representations of $\winf$ are known. This approach has the appeal of being mathematically complete and physically intuitive, encoding the picture suggested by Luttinger's theorem.

13 pages, plain LaTeX, no figures.

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Cited by in corpus (14)

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• Characterization of One-Dimensional Luttinger Liquids in Terms of Fractional Exclusion Statistics
• Algebraic bosonization: the study of the Heisenberg and Calogero-Sutherland models
• G(2)-Calogero-Moser Lax operators from reduction
• Dynamical symmetry algebra of the Calogero model
• Quantum fluctuations of the Chern-Simons theory and dynamical dimensional reduction
• Truncated Calogero-Sutherland Models on a Circle
• Effective short distance interaction in Calogero-Sutherland quantum fluids
• Laminar flow of charged quantum fluids of the Calogero-Sutherland universality class
• Quantum dynamics of the effective field theory of the Calogero-Sutherland model
• Dynamic structure factor of Calogero-Sutherland fluids
• A new class of Matrix Models arising from the W-infinity Algebra
• Bosonic Bogoliubov transformations as Lorentz boosts in $(c,\overline{c})=(1,1)$ conformal field theories with marginal $J\overline{J}$ deformations